The topic of identity seems to many of us to be philosophically unproblematic. Identity, we will say, is the relation that each thing has to itself and to nothing else.

Of course, there are many disputable claims that one can make using a predicate that expresses the identity relation. For example: there is something that was a man and is identical to God; there is something that might have been a poached egg that is identical to some philosopher.

But puzzling as these claims may be, it is not the identity relation that is causing the trouble. The lesson appears to be a general one. Puzzles that are articulated using the word 'identity' are not puzzles about the identity relation itself.

One may have noticed that our gloss on identity as 'the relation that each thing has to itself and to nothing else' was not really an analysis of the concept of identity in any reasonable sense of 'analysis', since an understanding of 'itself' and 'to nothing else' already requires a mastery of what identity amounts to. But the appropriate response, it would seem, is not to search for a 'real analysis' of identity; rather, it is to admit that the concept of identity is so basic to our conceptual scheme that it is hopeless to attempt to analyse it in terms of more basic concepts.

Why is the concept of identity so basic? The point is not that we have inevitable need for an 'is' of identity in our language. Our need for the concept of identity far outstrips our need to make explicit claims of identity and difference. Consider, for example the following two simple sentences of first-order predicate logic:

∃x∃y(Fx and Gy) ∃x(Fx and Gx).

Both require that there be at least one thing in the domain of the existential quantifier that is F and that there be at least one thing in the domain of the existential quantifier that is G. But the second sentence makes an additional requirement: that one of the things in the domain that is F be identical to one of the things in the domain that is G.

Without mastery of the concept of identity it is not clear how we would understand the significance of the recurrence of a variable within the scope of a quantifier. In this vein, Quine observes that 'Quantification depends upon there being values of variables, same or different absolutely...' (Quine 1964:101). Similar remarks apply to sentences of natural language. By way of bringing out the ubiquity of the notion of identity in our language, Peter Geach notes of the pair of sentences 'Jim wounded a lion and Bill shot it' and 'Jim wounded a lion and BUI shot another (lion) dead' that the first expresses identity and the second diversity (Geach 1991: 285).